R help - Jul 2017 - Quadratic function with interaction terms for the PLS fitting model?

Dear all,

I am using the pls package of R to perform partial least square on a set of
multivariate data.  Instead of fitting a linear model, I want to fit my
data with a quadratic function with interaction terms.  But I am not sure
how.  I will use an example to illustrate my problem:

Following the example in the PLS manual:
## Read data
 data(gasoline)
gasTrain <- gasoline[1:50,]
## Perform PLS
gas1 <- plsr(octane ~ NIR, ncomp = 10, data = gasTrain, validation =
"LOO")

where octane ~ NIR is the model that this example is fitting with.

NIR is a collective of variables, i.e. NIR spectra consists of 401 diffuse
reflectance measurements from 900 to 1700 nm.

Instead of fitting with predict.octane[i] = a[0] * NIR[0,i] + a[1] *
NIR[1,i] + ...
I want to fit the data with:
predict.octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + ... +
b[0]*NIR[0,i]*NIR[0,i] + b[1] * NIR[0,i]*NIR[1,i] + ...

i.e. quadratic with interaction terms.

But I don't know how to formulate this.

May I have some help please?

Thanks,

Kelvin

	[[alternative HTML version deleted]]

> On Jul 12, 2017, at 6:58 PM, Ng, Kelvin Sai-cheong <kscng at
connect.hku.hk> wrote:
> 
> Dear all,
> 
> I am using the pls package of R to perform partial least square on a set of
> multivariate data.  Instead of fitting a linear model, I want to fit my
> data with a quadratic function with interaction terms.  But I am not sure
> how.  I will use an example to illustrate my problem:
> 
> Following the example in the PLS manual:
> ## Read data
> data(gasoline)
> gasTrain <- gasoline[1:50,]
> ## Perform PLS
> gas1 <- plsr(octane ~ NIR, ncomp = 10, data = gasTrain, validation =
"LOO")
> 
> where octane ~ NIR is the model that this example is fitting with.
> 
> NIR is a collective of variables, i.e. NIR spectra consists of 401 diffuse
> reflectance measurements from 900 to 1700 nm.
> 
> Instead of fitting with predict.octane[i] = a[0] * NIR[0,i] + a[1] *
> NIR[1,i] + ...
> I want to fit the data with:
> predict.octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + ... +
> b[0]*NIR[0,i]*NIR[0,i] + b[1] * NIR[0,i]*NIR[1,i] + ...
> 
> i.e. quadratic with interaction terms.
> 
> But I don't know how to formulate this.
I did not see any terms in the model that I would have called interaction terms.
I'm seeing a desire for a polynomial function in NIR. For that purpose, one
might see if you get satisfactory results with:

gas1 <- plsr(octane ~NIR + I(NIR^2), ncomp = 10, data = gasTrain, validation
= "LOO")
gas1

I first tried using poly(NIR, 2) on the RHS and it threw an error, which raises
concerns in my mind that this may not be a proper model. I have no experience
with the use of plsr or its underlying theory, so the fact that this is not
throwing an error is no guarantee of validity. Using this construction in
ordinary least squares regression has dangers with inferential statistics
because of the correlation of the linear and squared terms as well as likely
violation of homoscedasticity.

-- 
David.

> 
> May I have some help please?
> 
> Thanks,
> 
> Kelvin
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA

poly(NIR, degree = 2) will work if NIR is a matrix, not a data.frame.
The degree argument apparently  *must* be explicitly named if NIR is
not a numeric vector. AFAICS, this is unclear or unstated in ?poly.


-- Bert

Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Thu, Jul 13, 2017 at 10:15 AM, David Winsemius
<dwinsemius at comcast.net> wrote:
>
>> On Jul 12, 2017, at 6:58 PM, Ng, Kelvin Sai-cheong <kscng at
connect.hku.hk> wrote:
>>
>> Dear all,
>>
>> I am using the pls package of R to perform partial least square on a
set of
>> multivariate data.  Instead of fitting a linear model, I want to fit my
>> data with a quadratic function with interaction terms.  But I am not
sure
>> how.  I will use an example to illustrate my problem:
>>
>> Following the example in the PLS manual:
>> ## Read data
>> data(gasoline)
>> gasTrain <- gasoline[1:50,]
>> ## Perform PLS
>> gas1 <- plsr(octane ~ NIR, ncomp = 10, data = gasTrain, validation =
"LOO")
>>
>> where octane ~ NIR is the model that this example is fitting with.
>>
>> NIR is a collective of variables, i.e. NIR spectra consists of 401
diffuse
>> reflectance measurements from 900 to 1700 nm.
>>
>> Instead of fitting with predict.octane[i] = a[0] * NIR[0,i] + a[1] *
>> NIR[1,i] + ...
>> I want to fit the data with:
>> predict.octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + ... +
>> b[0]*NIR[0,i]*NIR[0,i] + b[1] * NIR[0,i]*NIR[1,i] + ...
>>
>> i.e. quadratic with interaction terms.
>>
>> But I don't know how to formulate this.
>
> I did not see any terms in the model that I would have called interaction
terms. I'm seeing a desire for a polynomial function in NIR. For that
purpose, one might see if you get satisfactory results with:
>
> gas1 <- plsr(octane ~NIR + I(NIR^2), ncomp = 10, data = gasTrain,
validation = "LOO")
> gas1
>
> I first tried using poly(NIR, 2) on the RHS and it threw an error, which
raises concerns in my mind that this may not be a proper model. I have no
experience with the use of plsr or its underlying theory, so the fact that this
is not throwing an error is no guarantee of validity. Using this construction in
ordinary least squares regression has dangers with inferential statistics
because of the correlation of the linear and squared terms as well as likely
violation of homoscedasticity.
>
> --
> David.
>
>
>>
>> May I have some help please?
>>
>> Thanks,
>>
>> Kelvin
>>
>>       [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius
> Alameda, CA, USA
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.